A comparative study between some bisection based partitions in 3D

Abstract

In the last years many different strategies have been developed to locally refine triangular and tetrahedral meshes. In three dimensions, many algorithms can be seen as a generalization of their respective counterparts in two dimensions. In this paper we study and compare three of the main algorithms used in the literature for the refinement of tetrahedral grids: Rivara–Levin, Plaza–Carey and Liu–Joe. We find out whether they are equivalent or not, and in what conditions the quality of the tetrahedra is also compared. We present numerical examples that support our study and that provide to engineers with practical notes for their numerical applications.